Comparative study of multi-objective metaheuristics

HV quality indicator

	NSGAII	NSGAIIDE	MOEAD	MOEADDE	SMPSO	SMSEMOA	SMSEMOADE	Friedman
ZCAT1	4.5739e-01	4.4856e-01	3.8236e-01	4.5528e-01	4.7225e-01	4.6443e-01	4.5594e-01	+
ZCAT2	7.4821e-01	6.8265e-01	7.1347e-01	7.4178e-01	7.5774e-01	7.5279e-01	6.9481e-01	+
ZCAT3	4.5423e-01	4.4184e-01	3.9152e-01	4.5397e-01	4.6008e-01	4.6266e-01	4.5025e-01	+
ZCAT4	4.5787e-01	4.4207e-01	3.8360e-01	4.5228e-01	4.5377e-01	4.6526e-01	4.5420e-01	+
ZCAT5	8.3976e-01	7.9271e-01	7.9626e-01	8.4084e-01	8.4572e-01	8.4525e-01	7.8059e-01	+
ZCAT6	4.7590e-01	3.5111e-01	4.0893e-01	4.7389e-01	4.5857e-01	4.7479e-01	3.7197e-01	+
ZCAT7	4.6850e-01	3.3128e-01	4.0623e-01	4.4802e-01	4.6750e-01	4.6846e-01	3.6666e-01	+
ZCAT8	1.8032e-01	1.3878e-01	1.0475e-01	1.7424e-01	1.8370e-01	1.8420e-01	1.5374e-01	+
ZCAT9	1.8221e-01	1.5072e-01	9.3748e-02	1.7621e-01	1.9328e-01	1.8579e-01	1.6165e-01	+
ZCAT10	3.8785e-02	0.0000e+00	7.0956e-04	2.8182e-02	3.4216e-02	4.0012e-02	0.0000e+00	+
ZCAT11	4.6748e-01	4.0678e-01	4.0947e-01	4.5408e-01	4.6636e-01	4.7310e-01	4.1065e-01	+
ZCAT12	4.6409e-01	3.9089e-01	3.9663e-01	4.5612e-01	4.7046e-01	4.7264e-01	4.0000e-01	+
ZCAT13	5.8764e-01	4.8620e-01	5.1889e-01	5.6819e-01	5.9134e-01	5.9074e-01	4.7756e-01	+
ZCAT14	2.9580e-01	2.8157e-01	2.0431e-01	2.9214e-01	3.0711e-01	3.0294e-01	2.8382e-01	+
ZCAT15	4.7103e-01	4.0621e-01	3.9293e-01	4.5679e-01	4.7633e-01	4.7473e-01	3.9595e-01	+
ZCAT16	3.4716e-01	3.0437e-01	2.4772e-01	3.2833e-01	3.5259e-01	3.5141e-01	2.8733e-01	+
ZCAT17	8.4152e-01	7.8311e-01	7.8492e-01	8.4281e-01	8.5697e-01	8.4525e-01	8.0338e-01	+
ZCAT18	4.6617e-01	2.8884e-01	4.1328e-01	4.4039e-01	4.6751e-01	4.7255e-01	3.2445e-01	+
ZCAT19	4.6385e-01	4.4182e-01	3.8857e-01	4.5455e-01	4.6030e-01	4.6873e-01	4.3736e-01	+
ZCAT20	4.6348e-01	3.2103e-01	4.0914e-01	4.4166e-01	4.6504e-01	4.6649e-01	3.7100e-01	+

Wilcoxon rank-sum test table

	NSGAIIDE	MOEAD	MOEADDE	SMPSO	SMSEMOA	SMSEMOADE
NSGAII	++++++++++++++++++++	++++++++++++++++++++	=+====+++++=++++=+++	-====+==-===========	-----==--=--=-==---=	=+==++++++++++++++++
NSGAIIDE		+-++=--++-==-+=+=-+-	=-=-----------------	--------------------	--------------------	===-===-=======+-===
MOEAD			--------------------	--------------------	--------------------	-=--=++--====-=-=+-+
MOEADDE				--==-+==-=-=--=-=-=-	-----==---------=---	=+==+++++++++=++++++
SMPSO					=====-==+===========	+++=+++=++++++++++++
SMSEMOA						++++++++++++++++++++

Critical distance ranking

Boxplot + Pareto Fronts for each problem